Evaluation of the Pseudosteady-State Method for Composite Systems in Various Flow Geometries

ABSTRACT The pseudosteady state method, as applied to radial composite systems, has been used to estimate swept region volumes for thermal recovery projects with a good degree of success. However, the increasing scope and complexity of thermal recovery projects, as well as, the general heterogeneity of petroleum reservoirs, have necessitated the consideration of different flow geometries other than radial. Using analytical solutions, this study seeks to evaluate the applicability of the pseudosteady state method to composite systems in radial, linear, elliptical and spherical flow geometries. To compare the solutions for the different flow geometries, the dimensionless pressure and time values have been normalized to account for the different definitions for dimensionless variables in each system. Results of the study indicate that, for the same mobility and storativity contrasts between the inner and outer regions, the dimensionless pressure derivatives for the four flow geometries can be collapsed into one curve during the period when the various systems approximate pseudosteady state flow. This observation confirms the pseudosteady state method as being independent of the regularly-shaped swept region shape. Results also show that the pseudosteady state flow period begins at the same time for all four flow geometries. However, the time to the end of pseudosteady state varies. The linear flow geometry shows the longest pseudosteady state flow period, while the spherical flow geometry shows the shortest. The radial and elliptical flow geometries show the same duration of pseudosteady state flow. The conditions under which a pseudosteady state flow period of a reasonable duration will occur for each of the four flow geometries are presented. Times for the start and end of the pseudosteady state flow period for each flow geometry, as functions of mobility and storativity contrasts, are also discussed. This study will help to identify the conditions under which the pseudosteady state method can be used to estimate the swept volume for thermal recovery projects under various reservoir situations.